A random point field related to Bose–Einstein condensation

Abstract

The random point fields which describe the position distributions of the systems of ideal boson gas in states of Bose-Einstein condensations are obtained through the thermodynamic limits. The resulting point fields are given by convolutions of two kinds of independent point fields: the so-called boson processes whose generating functionals are represented by the inverses of the Fredholm determinants for operators related to the heat operator and the point fields whose generating functionals are represented by the resolvents of the operators. The construction of the latter point fields in an abstract formulation is also given.

Large deviation principle for noninteracting boson random point processes

“…In Ref. 17, the random boson point fields, which describe the position distribution of the constituent particles for the ideal gas in the Bose-Einstein condensation ͑BEC͒ regime, are constructed for the first time.…”

“…The study of the RPF for the BEC is an interesting and delicate mathematical problem, 17 see also a recent paper. 4 It is known that the point process corresponding to the boson RPF is a Cox process driven by the square norm of a Gaussian process.…”

“…17 to describe the BEC in the ideal ͑noninteracting͒ boson gas. For the detailed presentation of these notions, we refer to Ref.…”

“…for any non-negative continuous function f and any bounded measurable set ⌳ ʛ supp f. It was shown 17 that for R = R d the boson random point process for the ideal Boson gas is described in the region of BEC ͑ Ͼ c ͒ by convolution of two measures: …”

Mean-field interacting boson random point fields in weak harmonic traps

“…20 The RPF describing a homogeneous Bose-Einstein condensation has been studied for the first time in Ref. 19, where the RPF is given by the convolution of usual boson RPF and another RPF. The latter one seems to describe position distribution of the condensed part of the constituent bosons.…”